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 A318016 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 8

%I #4 Aug 12 2018 19:37:16

%S 1,2,2,4,8,4,8,28,28,8,16,97,118,97,16,32,338,508,508,338,32,64,1178,

%T 2130,3062,2130,1178,64,128,4105,8971,17703,17703,8971,4105,128,256,

%U 14305,37700,103633,133136,103633,37700,14305,256,512,49850,158613

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ...1.....2......4........8........16..........32...........64...........128

%C ...2.....8.....28.......97.......338........1178.........4105.........14305

%C ...4....28....118......508......2130........8971........37700........158613

%C ...8....97....508.....3062.....17703......103633.......603215.......3512154

%C ..16...338...2130....17703....133136.....1033121......7960400......61442813

%C ..32..1178...8971...103633...1033121....10674882....109443619....1125607630

%C ..64..4105..37700...603215...7960400...109443619...1493271874...20443576030

%C .128.14305.158613..3512154..61442813..1125607630..20443576030..372575745070

%C .256.49850.667178.20446744.473867122.11570430384.279709797313.6788774522485

%H R. H. Hardin, <a href="/A318016/b318016.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

%F k=2: a(n) = 4*a(n-1) -2*a(n-2) +a(n-3) -a(n-4)

%F k=3: [order 11] for n>14

%F k=4: [order 26] for n>29

%F k=5: [order 61] for n>65

%e Some solutions for n=5 k=4

%e ..0..0..0..1. .0..0..0..0. .0..1..0..1. .0..0..0..0. .0..1..0..1

%e ..0..1..1..0. .0..0..0..1. .1..0..1..1. .0..0..0..0. .1..0..0..0

%e ..1..1..0..1. .0..0..0..1. .0..0..1..1. .1..1..1..1. .0..0..1..1

%e ..0..0..0..1. .0..0..0..1. .0..0..0..0. .1..1..1..1. .1..1..1..1

%e ..0..0..0..0. .1..0..0..0. .1..0..1..1. .0..0..0..0. .1..1..1..1

%Y Column 1 is A000079(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Aug 12 2018

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Last modified October 3 09:00 EDT 2023. Contains 365854 sequences. (Running on oeis4.)